Let f x - sin 3 x - sin 3 x - 2 - 3 - sin 3 x - 4 - 3 then the primitive of fx w-r-t- x is

f( x ) =sin ^ 3 x +sin ^ 3 ( x+ 2π #160; / 3 #160; ) #160; +sin ^ 3 ( x+ 4π #160; / 3 #160; ) #160; = 3sin x #160; / 4 sin 3x ...

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Sum of n Terms

Let f x = s...

Question

Let $f (x) = {sin}^{3} x + {sin}^{3} (x + \frac{2 π}{3}) + {sin}^{3} (x + \frac{4 π}{3})$ then the primitive of $f (x)$ w.r.t. $x$ is

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f (x) = {sin}^{3} x + {sin}^{3} (x + \frac{2 π}{3}) + {sin}^{3} (x + \frac{4 π}{3})

f (x)

x

C

{sin}^{3} x + {sin}^{3} (x + \frac{2 π}{3}) + {sin}^{3} (x + \frac{4 π}{3}) = 3 sin x sin (x + \frac{2 π}{3}) \cdot sin (x + \frac{4 π}{3})

a + b + c = 0

a^{3} + b^{3} + c^{3} = 3 a b c

\int_{0}^{2 π} {sin}^{3} x d x = 0

f (x) = {sin}^{3} x

f (- x) = - f (x)

\int \frac{sin 2 x}{sin 5 x sin 3 x} d x = \frac{1}{3} log | sin 3 x | - f (x)

f (x) =

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